Question

a radar sends slow moving a signal of frequency 8×1000000000 Hz towards an aircraft approaching the radar. If the reflected wave shows frequency shift 2000 Hz the speed with which the aircraft is approaching the radar is(velocity of radar signal is 300000000m/s)

Answer 1

velocity of radar signal, v = 3 × 10^8 m/s

frequency of radar signal, f = 8 × 10^9 Hz

a/c to question,

reflected wave shows frequency shift 2000 Hz.

frequency after reflection of radar signal , f' = $\frac{v+u}{v-u}f$ [from Doppler's effect ]

where speed of aircraft is u m/s

now, frequency shift = 2000Hz

or, (v + u)/(v - u)f - f = 2000

or, (v + u - v + u)/(v - u) f = 2000

or, 2uf/(v - u) = 2000

or, 2u × 8 × 10^9/(3 × 10^8 - u) = 2000

or, 8 × 10^6 u = 3 × 10^8 - u

or, 3 × 10^8 = (8 × 10^6 + 1) u

or, u = 3 × 10^8/(8 × 10^6 + 1) = 37.49m/s

hence, speed of aircraft is 37.49 m/s